Quanta Image Sensor Quantum Random Number Generation

ABSTRACT

Some embodiments provide methods and apparatus for quantum random number generation based on a single bit or multi bit Quanta Image Sensor (QIS) providing single-photon counting over a time interval for each of an array of pixels of the QIS, wherein random number data is generated based on the number of photons counted over the time interval for each of the pixels.

RELATED APPLICATIONS

This application is a continuation of application Ser. No. 16/099,152,which is a national stage application under 35 U.S.C. § 371 ofInternational Application No. PCT/US2017/031456, filed May 5, 2017,which claims the benefit of U.S. Provisional Application No. 62/332,077,filed May 5, 2017, each of which is hereby incorporated herein byreference in its entirety.

BACKGROUND

The present disclosure generally relates to random number generation(RNGn), random number generation using photo-detectors, and moreparticularly to highly-random, non-deterministic, photon-emission-basedrandom number generation.

Generating high quality random numbers is becoming more and moreimportant for several applications such as Cryptography, scientificcalculations (Monte-Carlo numerical simulations), and gambling. With theexpansion of computers' fields of use and the rapid development ofelectronic communication networks, the number of such applications hasbeen growing quickly. Cryptography, for example, is one of the mostdemanding applications. It involves algorithms and protocols forensuring the confidentiality, the authenticity, and the integrity ofcommunications, which requires true random numbers for generatingencryption. High-quality random numbers, however, cannot be obtainedwith deterministic algorithms (e.g., a pseudo-random number generator(PRNG)); instead, an actual physical process may be relied on togenerate high-quality random numbers. The most reliable processes arequantum physical processes which are fundamentally random. In fact, theintrinsic randomness of subatomic particles' behavior at the quantumlevel is one of the few completely random processes in nature. By tyingthe outcome of a random number generator (RNG) to the random behavior ofa quantum particle, it is possible to guarantee a truly unbiased andunpredictable system, which may be referred to as a Quantum RandomNumber Generator (QRNG).

The emission of photons is a Poisson process and has been used as thesource of randomness in RNGn. Photon detectors used in previousphoton-emission-based RNGn technologies include single-photon avalanchediodes (SPADs) and conventional CMOS image sensors (CISs). SPADs canprovide single-photon detection capability and realize QRNGn based onphoton quantum effects, but the relatively large size (e.g., 7-20 μmpixel pitch in a SPAD array) limits the data output rate per unit areasize. Also, the high dark count rate (e.g., ˜1000 counts/sec) in SPADsdegrades the randomness quality. A conventional CIS is limited by arelatively high noise floor (e.g., >1 e−r.m.s.) in the readoutelectronics and does not have single-photon detection capability. Inthis case, the photon signal is significantly corrupted by read noise,and as read noise is also randomly distributed, the RNGn process using aconventional CIS is not fully quantum-effects based, thus limiting therandomness quality and stability of the output.

As such, there is a need for further developments and improvements inQRNGs to, for example, provide QRNGs that more fully exploit and/orrealize quantum-based randomness. And such developments and improvementsmay provide for increasing photon-counting accuracy, reducing noise,reducing dark current, increasing the output data rate, and/orincreasing scalability.

SUMMARY OF SOME EMBODIMENTS

To, for example, address at least one or more of the above-describedand/or other limitations of QRNGs, some embodiments of the presentdisclosure provide methods and apparatus for quantum random numbergeneration based on a single-bit or multi-bit Quanta Image Sensor (QIS)providing single-photon counting over a time interval for each of anarray of pixels of the QIS, wherein random number data is generatedbased on the number of photons counted over the time interval for eachof the pixels.

In some embodiments, a QRNG comprises (i) a QIS that includes an arrayof pixels, wherein each pixel is configured to convert a single photonincident on the pixel into a single photocharge-carrier (an electron ora hole) that is stored in the pixel, and wherein the QIS is configuredto readout from each pixel, with single-photocharge-carrier sensitivity(thereby providing for single-photon sensitivity), thephotocharge-carriers, if any, stored in the pixel within a timeinterval, so as to generate a pixel signal (e.g., an analog voltagesignal or a digital number/signal) corresponding to the number of storedphotocharge-carriers; and (ii) comparison circuitry configured tocompare (e.g., in the analog or digital domain), for each pixel, thepixel signal with a threshold level to generate for each pixel a bithaving a binary value that depends on whether or not the pixel signal isless than the threshold level or not less than the threshold level,wherein the binary values are substantially equiprobable based on thethreshold level, thereby providing for binary output data having highquality randomness (e.g., with bit entropy ˜1).

All or part of the comparison circuitry may be monolithically integratedwith the pixel array of the QIS; in some embodiments, the QIS readoutcircuitry may embrace or comprise the comparison circuitry.

In some embodiments, the QRNG may also comprise one or more of (i) aphoton source configured to generate the photons incident on the QISpixel array, (ii) an optical conditioner disposed such that photonsemitted by the photon source impinge on the optical conditioner prior toimpinging on the pixel array, and (iii) a randomness extractorconfigured to process data (e.g., the random output data, or digitalpixel signals) generated from readout of the QIS.

In various embodiments, the QRNG may include control circuitryconfigured to, for example, adjust or control one or more of, thethreshold level, the time interval over which the pixel accumulatesphotocharge-carriers, the photon source emission intensity, and/or theoptical conditioner, to maximize the randomness (e.g., according to thebit entropy metric) of the random number data generated by the QIS. Insome embodiments, such adjustment control may be based on, for example,monitoring the quanta exposure and/or measuring/monitoring therandomness of the generated random number data.

In accordance with some embodiments, the single-bit or multi-bit QIScomprises an array of pixels (e.g., jots), each pixel being configuredfor photoconversion of an incident photon into a correspondingphotocharge (e.g., electron (e−) or hole (h+)), and having sufficientin-pixel conversion gain, without in-pixel avalanche gain, to providefor readout of the photocharge with single-electron sensitivity andresolution, thereby providing for single-photon counting over the timeinterval. In-pixel conversion gain, according to various embodiments,may be at least 420 μV/charge-carrier (e− or h+), and may be more than500 μV/ charge-carrier (e− or h+), and may further be more than 1000μV/charge-carrier (e− or h+). And, in accordance with variousembodiments, the read noise associated with each QIS pixel is about 0.5charge carriers (e− or h+) rms or less, and may be about 0.3 e− or h+rmsor less, and may further be about 0.15 e− or h+rms or less. Each QISpixel may include a charge storage (accumulation) region configured tostore (accumulate) the photocharge that is generated in the pixel overthe time interval and that is readout from the pixel following the timeinterval. The full well charge storage capacity of the pixel storageregion may be vary depending on the implementation (e.g., single-bit ormulti-bit QIS, conversion gain, voltage limits on readout chain, targetthreshold level, etc.).

Throughout the description and claims, the following terms take at leastthe meanings explicitly associated herein, unless the context dictatesotherwise. The meanings identified below do not necessarily limit theterms, but merely provide illustrative examples for the terms. Thephrase “an embodiment” as used herein does not necessarily refer to thesame embodiment, though it may. In addition, the meaning of “a,” “an,”and “the” include plural references; thus, for example, “an embodiment”is not limited to a single embodiment but refers to one or moreembodiments. Similarly, the phrase “one embodiment” does not necessarilyrefer the same embodiment and is not limited to a single embodiment. Asused herein, the term “or” is an inclusive “or” operator, and isequivalent to the term “and/or,” unless the context clearly dictatesotherwise. The term “based on” is not exclusive and allows for beingbased on additional factors not described, unless the context clearlydictates otherwise.

In addition, as used herein, unless the context clearly dictatesotherwise, the term “coupled” refers to directly connected or toindirectly connected through one or more intermediate components and, insome contexts, may also denote or include electrically coupled, such asconductively coupled, capacitively coupled, and/or inductively coupled.Further, “conductively coupled” refers to being coupled via one or moreintermediate components that permit energy transfer via conductioncurrent, which is capable of including direct current as well asalternating current, while “capacitively coupled” refers to beingelectrostatically coupled through one or more dielectric media, andpossibly also via one or more intervening conductors (e.g., via a seriesof capacitive components), that permit energy transfer via displacementcurrent and not via direct current. Those skilled in the art willfurther understand that elements may be capacitively coupledintentionally or unintentionally (e.g., parasitically) and that in somecontexts, elements said to be capacitively coupled may refer tointentional capacitive coupling. In addition, those skilled in the artwill also understand that in some contexts the term “coupled” may referto operative coupling, through direct and/or indirect connection. Forinstance, a conductor (e.g., control line) said to be coupled to thegate of a transistor may refer to the conductor being operable tocontrol the gate potential so as to control the operation of thetransistor (e.g., switching the transistor between “on” and “off”states), regardless of whether the conductor is connected to the gateindirectly (e.g., via another transistor, etc.) and/or directly.

In this regard, for ease of reference, as used herein, two layers,regions, or other structures/elements may be referred to as being“adjacent” if they do not include one or more intervening layers,regions (e.g., doped regions), or other structures/elements. In otherwords, two layers, regions, or other structures/elements referred tospatially (e.g., “on,” “above,” “overlying,” “below,” “underlying,”etc.) with respect to each other may have one or more interveninglayers, regions, or other structures/elements; however, use of the term“adjacent” (or, similarly, “directly,” such as “directly on,” “directlyoverlying,” and the like) denotes that no intervening layers, regions,or other structures/elements are present.

It will be appreciated by those skilled in the art that the foregoingbrief description and the following description with respect to thedrawings are illustrative and explanatory of some embodiments of thepresent invention, and are neither representative nor inclusive of allsubject matter and embodiments within the scope of the presentinvention, nor intended to be restrictive or characterizing of thepresent invention or limiting of the advantages which can be achieved byembodiments of the present invention, nor intended to require that thepresent invention necessarily provide one or more of the advantagesdescribed herein with respect to some embodiments. Thus, theaccompanying drawings, referred to herein and constituting a parthereof, illustrate some embodiments of the invention, and, together withthe detailed description, serve to explain principles of someembodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects, features, and advantages of some embodiments of the invention,both as to structure and operation, will be understood and will becomemore readily apparent in view of the following description ofnon-limiting and non-exclusive embodiments in conjunction with theaccompanying drawings, in which like reference numerals designate thesame or similar parts throughout the various figures, and wherein:

FIG. 1 schematically depicts a high-level block diagram of anillustrative Quanta Image Sensor (QIS) Quantum Random Number Generator(QRNG), in accordance with some embodiments according to the presentdisclosure; and

FIG. 2 depicts an illustrative example of an output signal distributionand binary data conversion in connection with implementing a QIS QRNG,in accordance with some embodiments according to the present disclosure.

DETAILED DESCRIPTION OF SOME EMBODIMENTS

In accordance with some embodiments according to the present disclosure,random numbers are generated based on a Quanta Image Sensor (QIS)providing single-photon detection of photons emitted from a photonsource having Poisson photon-emission statistics, wherein for each QISpixel (e.g., jot) the number of photons detected by the QIS pixel withina time interval is the quantum random variable used for quantum randomnumber generation (QRNGn). As will be understood by those skilled in theart in view of the present disclosure, such QIS QRNGn embodimentsovercome (among other things) limitations of known SPAD-based andconventional CIS-based random number generators (RNGs) (e.g., such aslimitations discussed above), and provide for quality quantum randomnumber generation.

And, more particularly, as will be understood in view of the ensuingdescription, in some embodiments of a QIS quantum random numbergenerator (QRNG) according to the present disclosure, each pixel (e.g.,jot) of the QIS QRNG provides for generating a random number based on acomparison between a threshold (e.g., threshold Ut in hereinbelowillustrative embodiments) and a signal that is generated by reading outthe pixel and that corresponds to a number of individual photonsdetected by the pixel within a given time interval.

For a given average number of photoelectrons collected in each jot pergiven time interval (e.g., frame), referred to herein as the quantaexposure (H), the threshold may be selected such that the probability ofthe signal being less than the threshold is equal (or substantiallyequal) to the probability of the signal being greater than or equal tothe threshold, thus providing for high quality binary quantum randomnumber generation. As will also be understood in view of the presentdisclosure, in some embodiments, the threshold may be controlled (e.g.,dynamically, based on feedback) to ensure quality randomness in view of,for example, temporal fluctuations in the quanta exposure (e.g., due tovarying average emission intensity of the photon source). Alternativelyor additionally, the quanta exposure may be controlled to ensure qualityrandomness (e.g., by controlling the photon source emission rate and/orthe pixel integration time).

In addition, in some embodiments the random data generated from the QISoutput may be input to and processed by a randomness extractor toprovide random number data having further improved randomness qualities.The randomness quality of the random data output by the QIS may requiregreatly reduced post-processing (e.g., randomness extraction processing)compared to, for example, prior SPAD and CIS based RNGs. And, someembodiments may provide high quality quantum random number generationwithout requiring a randomness extractor.

Referring now to FIG. 1, depicted is a schematic, high-level blockdiagram of an illustrative QIS QRNG, in accordance with some embodimentsaccording to the present disclosure. As shown, the illustrative QIS QRNGembodiment comprises a photon source 12 and an optical conditioner 14under control of control circuitry 16, a Quanta Image Sensor (QIS) 20,and a randomness extractor 30. Photon source 12, conditioner 14, and QIS20 are configured (e.g., according to position/alignment, and/or use ofreflection, optical waveguiding (e.g., using an optical fiber or otherwaveguide structure), and/or other optical components) such that photonsemitted by source 12 impinge via optical conditioner 14 on a QIS pixelarray 21 of QIS 20. In various embodiments, QIS QRNG may be implementedmonolithically (e.g., formed on a common semiconductor substrate), or astwo or more separate chips (e.g., die) or other components. Forinstance, in some embodiments, photon source 12 may be formed on a firstdie, QIS 20 may be formed as a backside-illuminated imager on a seconddie, and extractor 30 (and possibly additional processing and/orbuffering circuitry) may be formed on a third die, with the first,second, and third dies vertically stacked (in sandwich-like fashion) andintegrated.

Photon source 12 may be implemented as any of various optical sourcesthat emits photons according to Poisson statistics, such as one or morelight emitting diodes (LEDs; e.g., an silicon (Si) LED device or Si LEDarray), or one or more laser diodes (e.g., driven with above-thresholddrive current). In such embodiments, for example, the intensity of thephoton signal emitted by photon source 12 may be controlled by circuitry16 according to the LED or laser drive current. Alternatively oradditionally, the photocarrier (e.g., photoelectron) rate generated inthe QIS may be adjusted based on the relative location of the photonsource to the pixel array, and in some embodiment this relative locationis configured to be controllable/adjustable (e.g., manually and/orautomatically (e.g., without user input)). In some embodiments, however,the photon source 12 (and any photon source control circuitry) may beindependent of the QIS QRNG apparatus; for example, in some suchembodiments photon source 12 may be an independent photon source, suchas a source of ambient light that may be detected by QIS 20. In otherwords, in such embodiments, the photon source may not be considered asbeing part of the QIS QRNG apparatus, although QIS QRNG embodimentsaccording to the present disclosure may be configured to include photonsource 12 as well as its drive/power and/or control circuitry.

Optical conditioner 14, which is an optional component, may be includedto provide additional control over the photon signal that impinges onthe QIS array 21. For example, optical conditioner may be a controllableattenuator, splitter, or the like.

QIS 20 is schematically depicted as comprising a pixel (e.g., jot) array21, a readout chain comprising a programmable gain amplifier (PGA) 22,correlated-double-sampling (CDS) circuitry 24, and analog-to-digitalconverter (ADC) 26, all under control of control circuitry 28, which mayalso be coupled with control circuitry 16 for purposes of coordinatedcontrol of photon source 12, optical conditioner 14, and QIS 20 inproviding a quality quantum random number data signal QRN1 output fromQIS 20 (e.g., by controlling H and/or Ut, as will be further understoodbelow). It will be understood that the simplified block diagram of QIS20 is set forth for clarity of exposition in describing the operation ofthe QIS QRNG with respect to readout of an individual pixel (jot) withinthe QIS pixel array 21, which may comprise around a billion or more(e.g., several billion) sub-diffraction limit pixels that may be readout row-wise in column-parallel manner, with each column of pixels beingassociated with a readout chain comprising PGA, CDS, and ADC circuitry(though, e.g., in some embodiments all columns may not be read out inparallel simultaneously as groups of two or more columns may sharereadout chain circuitry (e.g., such as sharing at least an ADC)). Inaddition, for example, QIS 20 may comprise additional circuitry, such asan output buffer and/or image/data processing circuitry coupled betweenthe output of ADC 26 and input to extractor 30 (e.g., by way ofnon-limiting example, data QRN1 may be input to a buffer that isaccessible to image/data processing circuitry that is configured toprocess QRN1 data and write the processed data back to the buffer foroutput to extractor 30).

Depending on the implementation, QIS 20 may be a single-bit QIS ormulti-bit QIS. Each pixel/jot of QIS 20 has single-electron sensitivity(e.g., ˜0.15e−r.m.s.) which may be obtained from high, in-pixelconversion gain, e.g., more than 500 μV/e−, and more than 10000 μV/e− insome embodiments. As described, QIS 20 may comprise at least one billionjots (at least 1 G-jot, such as several G-jots), though some embodimentsmay employ less than 1 G-jot (e.g., ˜0.1 G-jots or more). And thereadout speed may be more than 1000 fps, which yields an output datarate of (e.g., for a single-bit QIS) about 100 Gb/s to more than 1 Tb/s(e.g., several Tb/s). Depending on the application, the output data ratemay be varied according to the number of jots in the QIS array and/orthe readout scan rate may be varied.

The QIS jots may be implemented as pump-gate jots; however, any suitablejot device for implementing a single-bit or multi-bit QIS (e.g., havingsufficient conversion gain for single photocarrier detection) may beemployed. Additional aspects and details concerning implementations of aQIS in a QIS QRNG in accordance with embodiments of the presentdisclosure may be understood by those skilled in the art in view of, forexample, each of the following publications, each of which is herebyincorporated by reference herein in its entirety: (i) PCT internationalapplication publication no. WO/2015/153806 (corresponding to PCTinternational application no. PCT/US2015/023945), “CMOS Image Sensorwith Pump Gate and Extremely High Conversion Gain,” published Oct. 8,2015, (ii) J. Ma and E. R. Fossum, A Pump-Gate Jot Device with HighConversion Gain for Quanta Image Sensors, IEEE J. Electron DevicesSociety, vol. 3(2), pp. 73-77, March 2015, (iii) J. Ma and E. R. Fossum,Quanta image sensor jot with sub 0.3 e−r.m.s. read noise and photoncounting capability, IEEE Electron Device Letters, vol. 36(9), pp.926-928, September 2015, (iv) J. Ma, D. Starkey, A. Rao, K. Odame, andE. R. Fossum, Characterization of quanta image sensor pump-gate jotswith deep sub-electron read noise, IEEE J. Electron Devices Society,vol. 3(6), pp. 472-480, November 2015, and (v) S. Masoodian, A. Rao, J.Ma, K. Odame and E. R. Fossum, A 2.5 pJ/b binary image sensor as apathfinder for quanta image sensors, IEEE Trans. Electron Devices, vol.63(1), pp. 100-105, January 2016.

As will be understood, readout of the jots in the QIS array 21 isanalogous to readout of accumulated charge from pixels in conventionalCISs. During readout, the jot output signal (e.g., output from an in-jotsource-follower amplifier, not shown) corresponding to the chargeaccumulated in the jot may be coupled to a column bus (e.g.,corresponding to the input to PGA 22), resulting in a correspondinganalog signal being coupled to the input of ADC 26 via PGA 22 and CDS 24circuitry. ADC 26 converts the input analog signal into an n-bit digitalsignal.

In a single-bit QIS, the bit width (n) is one (1), and the binary outputof the ADC corresponds to whether or not the analog signal input to theADC 26 from CDS 24 (the “ADC signal input”) is less than Ut or not lessthan Ut. As described above, and as may be further understood in view ofthe ensuing disclosure (as well as the Appendix of priority U.S.Provisional Application No. 62/332,077, filed May 5, 2017, which ishereby incorporated herein by reference in its entirety), Ut may beselected such that these cases are equiprobable, thus providing for thebinary output (e.g., QRN1) having high quality randomness (e.g., withbit entropy ˜1) based on the quantum optical randomness of the photonsource.

In some multi-bit QIS embodiments, the bit width (n) may be an integervalue between, for example, two and about 6 (e.g., 1≤n≤6). In some suchembodiments, the LSB may correspond to one photoelectron. It will beunderstood, however, that in various alternative embodiments, it is alsopossible to configure the ADC such that the LSB is less than theequivalent of one photoelectron (e.g., 0.2 electrons). Some multi-bitQIS embodiments may employ more than 6 bits, and the DN output by theADC may be linearly scaled over the range of the analog signal rangeinput to the ADC based on the number of photoelectrons that can bedetected/counted by the jot, the readout noise, and the gain (e.g., jotconversion gain, PGA gain).

In some embodiments, control circuitry 28 may provide threshold Ut as ananalog signal to ADC 26 (e.g., control circuitry 28 may convert adigital Ut signal to the analog Ut signal; or Ut may originate as ananalog signal in control circuitry 28), which may compare the thresholdUt in the analog domain to the analog signal input to the ADC 26 fromCDS 24 (the “ADC signal input”), and output a binary value (e.g., “0” or“1”) according to whether the ADC signal input is less than Ut or notless than Ut. Similarly, such analog domain comparison may beimplemented wherein control circuitry 28 provides a digital Ut value toADC 24, which may comprise digital-to-analog converter (DAC) circuitryto convert Ut to an analog signal.

In some embodiments, the comparison with Ut may be executed in thedigital domain. For example, ADC 26 may convert the ADC signal inputinto an multi-bit digital number (DN). That multi-bit digital number maybe compared with a digital representation of Ut (e.g., which may begenerated from an analog Ut signal, or may originate as a digitalvalue), and a binary value may be generated based on whether the DN isless than or not less than Ut. It will be understood that such digitalcomparison may be implemented within the QIS (e.g., in circuitryfollowing the ADC output (not shown); or, in some implementations, suchcircuitry may also be embodied in (or considered as being logically partof) ADC 26). Alternatively, for example, such digital comparisoncircuitry may be implemented external to (e.g., off-chip) from the QIS,and may be embodied within the extractor 30 in some embodiments.

Accordingly, in some multi-bit QIS embodiments, the output of the ADCmay be a multi-bit digital number (DN) (e.g., representing the ADC inputsignal) that may be provided to additional circuitry to generate asingle-bit random number bit stream based on comparison with a thresholdvalue. And, in some multi-bit QIS embodiments, the output of the ADC maybe a single-bit random number bit stream (e.g., where the ADCincorporates digital-domain comparison circuitry).

As noted, in some embodiments, such post-ADC digital-domain comparisoncircuitry may be embodied in randomness extractor 30, which may furtherprocess the random number bit stream to provide a random numberbitstream QRN2 having improved randomness using techniques known tothose skilled in the art (e.g., compression algorithms based on hashingand/or matrix multiplication). In some embodiments, however, randomnessextractor 22 may not be required (and thus may not be included as partof QIS QRNG). For example, QIS QRNG may be configured to periodically oraperiodically adjust/control one or more of, for example, the thresholdvalue (Ut), the jot detection time interval, and the photon sourceemission intensity to maximize the randomness (e.g., according to thebit entropy metric) of the generated random number data (e.g., QRN1). Insome embodiments, such adjustment control may be based on, for example,monitoring the quanta exposure and/or measuring/monitoring therandomness of the generated random number data.

Design and operational principles for implementing a QIS QRNG accordingto some embodiments of the present disclosure may be further understoodin view of the following, as well as in view of the Appendix of priorityU.S. Provisional Application No. 62/332,077, filed May 5, 2017, which ishereby incorporated herein by reference in its entirety.

In a QIS (as in a conventional CIS), the photon signal is converted to avoltage signal in one pixel/jot and corrupted with noise in the readoutchain. The distribution of the output signal is a convolution betweenthe Poisson distribution of the arrival of photoelectrons and a normaldistribution of noise. An example of signal distribution is shown inFIG. 2. The average rate of photoelectrons is defined as quanta exposureH. In a single-bit QIS, an artificial threshold U_(t) (e.g., 0.5 e−) isset in the readout chain to convert the output signal to binary data:output signal higher than U_(t) will be converted into “1” and to “0”when it is below U_(t). The probability of “1” state is:

${P\left\lbrack {U < U_{t}} \right\rbrack} = {\sum\limits_{k = 0}^{\infty}{{\frac{1}{2}\left\lbrack {1 + {{erf}\left( \frac{U_{t} - k}{u_{n}\sqrt{2}} \right)}} \right\rbrack} \cdot \frac{e^{- H}H^{k}}{k!}}}$

where u_(n) is the read noise of the sensor, and the probability of “0”state is:

P[U≥U _(t)]=1−P[U<U _(t)]

Given a proper quanta exposure H (e.g. H<1), a 1-bit random number canbe generated from one readout of one jot. The QIS based random numbergenerator can include a QIS device and a stable light source (e.g., suchas described hereinabove in connection with embodiments according toFIG. 1 and some variations thereof). An ideal random number generator isexpected to generate “0 s” and “1 s” with equal probability; otherwise,an extractor may need to be applied to select the useful data. Theminimum entropy indicates the percentage of useful data, which is givenby:

S _(min)=−log₂[max(P([U≥U _(t) ], P[U<U _(t)])]

An entropy close to 1 is ultimately desired. To achieve that, a quantaexposure H=log_(e) (2) may be set up by the illumination condition(e.g., light source, packaging, QIS integration time).

As noted above, further description of a QIS QRNG, including itsprinciples of operation, according to some embodiments of the presentdisclosure is presented in the Appendix of priority U.S. ProvisionalApplication No. 62/332,077, filed May 5, 2017, which is herebyincorporated herein by reference in its entirety, which Appendix is setforth as an article entitled “Quantum Random Number Generation UsingQuanta Image Sensor,” which illustrates some embodiments of the presentinvention as well as various features and advantages that may beassociated with some embodiments, and is not intended to limit thepresent invention.

In view of the present disclosure, it will be understood that a QIS QRNGprovides many features and advantages that, among other things, overcomelimitations of known SPAD and conventional CIS based RNGs. For example,as discussed, a QIS may include, for example, 100 Mjots to one or moreGiga-jots having photon-counting capability, with the jot array havingsubmicron pitch (e.g., 200 nm-500 nm), and the QIS can be readout at ahigh frame rate (1000 fps). Accordingly, these features (e.g., small jotsize and high speed) provide the QIS QRNG with extremely high dataoutput rate. And the photon-counting capability of jot device can ensurethe QRNG is fully photon quantum effects based. Further, the low darkcurrent (e.g., 0.1 e−/sec at room temperature) provides for improvedrandomness quality and stability. In short, some embodiments of aQIS-based QRNG device provides for, among other things, high data rate(e.g., 5-12 Gb/s), low dark current error, and high stability.

Accordingly, although the above description of illustrative embodimentsof the present invention, as well as various illustrative modificationsand features thereof, provides many specificities, these enablingdetails should not be construed as limiting the scope of the invention,and it will be readily understood by those persons skilled in the artthat the present invention is susceptible to many modifications,adaptations, variations, omissions, additions, and equivalentimplementations without departing from this scope and withoutdiminishing its attendant advantages. For instance, except to the extentnecessary or inherent in the processes themselves, no particular orderto steps or stages of methods or processes described in this disclosure,including the figures, is implied. In many cases the order of processsteps may be varied, and various illustrative steps may be combined,altered, or omitted, without changing the purpose, effect or import ofthe methods described. Similarly, the structure and/or function of acomponent may be combined into a single component or divided among twoor more components. It is further noted that the terms and expressionshave been used as terms of description and not terms of limitation.There is no intention to use the terms or expressions to exclude anyequivalents of features shown and described or portions thereof.Additionally, the present invention may be practiced without necessarilyproviding one or more of the advantages described herein or otherwiseunderstood in view of the disclosure and/or that may be realized in someembodiments thereof. It is therefore intended that the present inventionis not limited to the disclosed embodiments but should be defined inaccordance with claims that are based on the present disclosure, as suchclaims may be presented herein and/or in any patent applicationsclaiming priority to, based on, and/or corresponding to the presentdisclosure.

What is claimed is:
 1. A quantum random number generator (QRNG),comprising: a Quanta Image Sensor (QIS) comprising a pixel array,wherein each pixel of the QIS is configured to convert photons emittedfrom a photon source into photocarriers having electrical charge,wherein the QIS is configured to readout each pixel to provide a signalrepresenting a number of the photocarriers collected within a timeinterval with single-photocarrier sensitivity; and wherein the QRNG isconfigured to output random number data having randomness based on thenumber of collected photocarriers within the time interval, wherein foreach pixel the number of photocarriers collected within the timeinterval is converted to a voltage and then into a binary signal using athreshold level that can be adjusted by adjusting a reference voltage.2. The QRNG according to claim 1, wherein the voltage is compared to thethreshold level in the analog domain.
 3. The QRNG according to claim 1,wherein the conversion is performed in the digital domain, wherein thevoltage is converted to a digital signal or digital number (DN) by ananalog-to-digital converter (ADC) which has a bit depth higher than1-bit, and the digital signal or digital number is converted to a 1-bitrandom number.
 4. The QRNG according to claim 1, wherein a rate ofcollection of the photocarriers and the threshold level are tunable torealize a randomness entropy of the random number data that is idealand/or to realize greater than a minimum value of the randomness entropyof the random number data.
 5. The QRNG according to claim 1, wherein arate of collection of the photocarriers is capable of being adjustedbased on the relative location of the photon source to the pixel array.6. The QRNG according to claim 1, wherein the reference voltage issupplied by an on-chip or off-chip digital-to-analog converter (DAC). 7.The QRNG according to claim 1, wherein at least the threshold level isperiodically or aperiodically reset to maximize randomness entropy. 8.The QRNG according to claim 1, wherein one or more of the following areperiodically or aperiodially adjusted to maximize randomness entropy ofthe random number data: the time interval over which the photocarriersare collected, an intensity of the photon source, and the thresholdlevel used to determine the value of the binary signal.
 9. The QRNGaccording to claim 1, wherein the QRNG includes the photon source. 10.The QRNG according to claim 1, wherein the QRNG includes a randomnessextractor.
 11. The QRNG according to claim 1, wherein the QRNG includesan optical conditioner disposed such that photons emitted by the photonsource impinge on the optical conditioner prior to impinging on thepixel array.
 12. The QRNG according to claim 1, wherein the photonsource has an intensity that is tunable to realize an ideal randomnessentropy of the random number data and/or to realize greater than aminimum value of the randomness entropy of the random number data.
 13. AQRNG, comprising: a Quanta Image Sensor (QIS) comprising an array ofjots that are each configured to provide single-photon detection ofphotons emitted from a photon source having Poisson photon-emissionstatistics, wherein each jot is configured with sufficient in-pixelconversion gain, and without in-pixel avalanche gain, to provide forreadout from the jot of an electrical signal representing a number ofphotons detected by the jot within a time interval, wherein theelectrical signal has single-charge sensitivity and resolutioncorresponding to single-photon sensitivity and resolution; and whereinthe QRNG is configured to output random number data, wherein for eachjot the number of photons detected by the jot within the time intervalis a quantum random variable used for generation of the random numberdata.
 14. A QRNG comprising: a QIS that includes an array of pixels,wherein each pixel is configured to convert each of at least one photonincident on the pixel into a respective photocharge-carrier that isstored in the pixel, and wherein the QIS is configured to readout fromeach pixel, with single-photocharge-carrier sensitivity, each of the atleast one respective photocharge-carriers, if any, stored in the pixelwithin a time interval, so as to generate a pixel signal correspondingto a number of photocharge-carriers stored in the pixel, wherein eachpixel has sufficient in-pixel conversion gain, without in-pixelavalanche gain, to provide for readout of the photocharge-carriers withsingle-charge sensitivity and resolution; and comparison circuitryconfigured to compare for each pixel, the pixel signal with a thresholdlevel to generate for each pixel a bit having a binary value thatdepends on whether or not the pixel signal is less than the thresholdlevel or not less than the threshold level, wherein the binary valuesare substantially equiprobable based on the threshold level, therebyproviding for binary output data having high quality randomness.
 15. TheQRNG according to claim 14, further comprising one or more of (i) aphoton source configured to generate photons incident on the QIS pixelarray, (ii) an optical conditioner disposed such that photons emitted bythe photon source impinge on the optical conditioner prior to impingingon the pixel array, and (iii) a randomness extractor configured toprocess data generated from readout of the QIS.
 16. The QRNG accordingto claim 15, wherein the QRNG includes control circuitry configured toadjust or control at least one of (i) the threshold level, (ii) the timeinterval, (iii) the photon source emission intensity, and (iv) theoptical conditioner, to maximize the randomness of the binary outputdata generated by the QRNG.
 17. The QRNG according to any one of claims14, wherein each pixel has an associated read noise that is at least oneof 0.5 charge carriers rms or less, 0.3 charge carriers rms or less, and0.15 charge carriers rms or less.
 18. A method for quantum random numbergeneration, the method comprising: generating for each of a plurality ofpixels of a single-bit or multi-bit Quanta Image Sensor (QIS) a signalrepresenting a number of individual photons incident on the pixel over atime interval, said signal being generated without in-pixel avalanchegain; and generating random number data based on a plurality of thesignals, each of the signals representing the number of photons detectedover the time interval for a respective one of the pixels, wherein saidnumber of photons detected over the time interval for each of the pixelsvaries as a quantum random variable.
 19. A QRNG, comprising: a QuantaImage Sensor (QIS) comprising an array of jots that are each configuredto provide single-photon detection of photons emitted from a photonsource having Poisson photon-emission statistics, wherein each jot isconfigured with sufficient in-pixel conversion gain, and withoutin-pixel avalanche gain, to provide for readout from the jot of anelectrical signal representing a number of photons detected by the jotwithin a time interval, wherein the electrical signal has single-chargesensitivity and resolution corresponding to single-photon sensitivityand resolution; and comparison circuitry configured to compare, for eachjot, the electrical signal with a threshold level, wherein the QRNG isconfigured to output random number data, wherein for each jot the numberof photons detected by the jot within the time interval is a quantumrandom variable used for generation of the random number data based onthe comparison of the electrical signal with the threshold level.